Computing the degrees of freedom of rank-regularized estimators and cousins
Name
20-EJS1681.pdf
Description
Published version
Size
1.08 MB
Format
Adobe PDF
Checksum (MD5)
e78e4a0a626d4594e082ffd339156957
Author(s)
Mazumder, Rahul
Weng, Haolei
Date Issued
2020
Journal
Electronic Journal of Statistics
Publisher
Institute of Mathematical Statistics
Version
Final published version
Abstract
Estimating a low rank matrix from its linear measurements is a problem of central importance in contemporary statistical analysis. The choice of tuning parameters for estimators remains an important challenge from a theoretical and practical perspective. To this end, Stein’s Unbiased Risk Estimate (SURE) framework provides a well-grounded statistical framework for degrees of freedom estimation. In this paper, we use the SURE framework to obtain degrees of freedom estimates for a general class of spectral regularized matrix estimators-our results generalize beyond the class of estimators that have been studied thus far. To this end, we use a result due to Shapiro (2002) pertaining to the differentiability of symmetric matrix valued functions, developed in the context of semidefinite optimization algorithms. We rigorously verify the applicability of Stein’s Lemma towards the derivation of degrees of freedom estimates; and also present new techniques based on Gaussian convolution to estimate the degrees of freedom of a class of spectral estimators, for which Stein’s Lemma does not directly apply.
MIT Department
Sloan School of Management
Massachusetts Institute of Technology. Operations Research Center
Terms of Use
Creative Commons Attribution 4.0 International license
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1214/20-EJS1681
